How and why do children form imaginary friends?

There are a few different reasons. It makes a difference how old the child is and how they use the mechanism of the "imaginary friend".

Very young children often develop imaginary friends in an attempt to broaden their social circles. They also use this mechanism to codify the social roles they see around them and on TV.

Slightly older children may be acting out some desire or fantasy. I had 8 imaginary kittens. I loved animals (still do) but was not allowed to have a cat in the house. It can also be a method for gaining a little attention (if mommy pays attention to me by holding the door open for me, she must also pay attention to me when she holds the door open for my friend).

After the earliest elementary ages, some other factors come to play. Children who feel outcast or different from their peers may develop an imaginary friend who is like them or who provides them with kindness, attention, understanding or support they feel they may not be getting elsewhere. They may use the imaginary friend to test out social scenarios in order to gain a feeling for what is normal or right or acceptable.

Children who have been abuse or witnessed stressful situations often use an imaginary friend as a protective sheild - a friend who will not fail them or hurt them. They may even speak through the friend when afraid to speak themselves.

For the most part, psychological development of imaginary friends as a young child is normal, so long as it does not fear w/ normal social interaction and development.

Well since I am not a psychologist or a psychology major this would only be my opinion and not proven fact. I thinkthe why is many times because they are an only child or are alienated by other children including their siblings so in order to compensate for that they form imaginary friends. Then also depending on how young they were it is possible some of their friends may not be imaginary at all but they may be able to see things more mature children or adults can't such as angels or spirits of those who have passed on and have not been able to move on to the other side. As for the how I really am not sure and would not even begin to attempt to venture a guess.